Jordan wrote that his first focus is maintaining Republican control of the House.

"After that, we can focus on filling the vacancy resulting from Speaker Ryan's retirement from Congress," he wrote. "At that time, I plan to run for Speaker of the House to bring real change to Congress."

In his letter, he emphasized his priorities of repealing the Affordable Care Act, building a security wall on the U.S.-Mexico border and fixing the "broken immigration system."

"Many believe that our congressional majorities have let them down," he wrote. "Beyond tax relief and regulatory reform, the American people want us to follow through with our promises."

Former wrestlers have accused Dr. Richard Strauss, the OSU wrestling team doctor from the mid-1970s to 1990s, of sexually assaulting them during his tenure with the team. Jordan, who was OSU’s assistant wrestling coach from 1986 to 1994, has said multiple times he was not aware of the abuse until players began speaking publicly about it earlier this year.

GOP lawmakers have come out in support of Jordan, including the conservative voting bloc the House Freedom Caucus, which he cofounded.

A group of former wrestlers and OSU coaches has also stated on the record that they do not believe Jordan knew about the abuse.

The articles of impeachment, signed with nine other GOP lawmakers, charge that Rosenstein has a conflict of interest in Mueller's probe, and obfuscated information for ongoing investigations into the FBI and DOJ's conduct during the 2016 presidential election.

Jordan on Wednesday night said he and Meadows believe Rosenstein has "stonewalled" efforts by Congress to obtain documents necessary for their investigations.

"We’re tired of the Justice Department giving us the finger and not giving us the information," he told Fox News host Laura Ingraham on her show, "The Ingraham Angle."